for suitable penalty parameters \(\lambda _1\)  and \(\lambda _2\) . [1]} considered the \(L_1\) -fusion estimator \(\hat{\theta }^F\)  with penalization of the successive differences only, given by,
\(\hat{\theta }^{F} = \arg \min _{\theta \in \mathbb {R}^n}\left\lbrace \dfrac{1}{2}\Vert y-\theta \Vert _2^2 + \lambda \Vert \eta \Vert _1\right\rbrace ,\) 
